Nuclear Radii by Scattering of Low-Energy Neutrons

Abstract

The potential scattering cross section for slow neutrons, ${\ensuremath{\sigma}}_{p}$, has been measured for seventeen elements in order to determine the nuclear potential radius and to investigate the predictions of nuclear optical models. The measurements were based on total cross sections resulting from transmission experiments performed with the Brookhaven fast chopper. In the energy region where individual resonances can be resolved and their parameters determined with reasonable accuracy, ${\ensuremath{\sigma}}_{p}$ is obtained by subtracting the resonance contribution, including interference effects, from the measured total cross section. In the kev region, where the chopper resolution permits determination of cross sections averaged over many resonances only, different sample thicknesses are used and ${\ensuremath{\sigma}}_{p}$ derived from the slope of the transmission curve. The results in the two energy regions agree, thereby justifying the concept of potential scattering as a cross section constant with energy, once effects of nearby resonances are removed. The variation of potential scattering with atomic weight is compared with predictions of optical models of the nucleus. The data reflect rather strongly the effects of the deformation of the nuclear shape from spherical, and good agreement is obtained for a potential well with a diffuse surface and nuclear deformations corresponding to known quadrupole moments. The radius of the potential (the distance to its half-value) is given by $R={r}_{0}{A}^{\frac{1}{3}}$, with ${r}_{0}=(1.35\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm. The radius parameter ${r}_{0}$ is thus distinctly larger than the 1.09\ifmmode\times\else\texttimes\fi{}${10}^{13}$ cm obtained from electron scattering experiments.